Why did non-monarchic rule meet with so little success in ancient China?You have to remember that Confucianism consisted of Ancestor worship and also fealty to the Father, as was explained to me the family got larger outside your kin. Keep following the "family" model up and father can go from your father, to mayor, to governor to Emperor. Legalism was against this, one of the reasons for the conflict, but not the only one.

Is the Cold War still going on?Agreed, if you look at how the term was used it was the state of affairs between Communism and Capitalism. Whatever else is going on now is basically "diplomacy by other means".